Graph theory worksheet with answers

Free printable Graph theory worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
ABCDEFG

Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 7
Σ deg =
2.Easy
ABCDE

Exactly one vertex of the graph has degree 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
3.Medium

How many different Hamilton circuits H does the complete graph K5 have? Circuits that differ only in the starting vertex or the direction count as the same.

K5
H =
4.Medium

A connected graph has 20 vertices and 29 edges. How many edges k must be removed to leave a spanning tree?

|V| = 20|E| = 29
k =
5.Hard
159178613204ABCDEF

Prim’s algorithm builds a minimum spanning tree starting from vertex E. Click the edge it adds as edge number 4.

start: Ek = 4
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge EF
  8. 8edge BE
6.Hard
7853101249ABCDEF

Use Dijkstra’s algorithm to find the length d(F) of the shortest path from A to F in the weighted graph.

start: Aend: F
d(F) =

Answer key

  1. 1. Σ deg = 16
  2. 2. C
  3. 3. H = 12
  4. 4. k = 10
  5. 5. edge AC
  6. 6. d(F) = 14

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